Explores transporters as a practical alternative to parallel transport, discussing minimal requirements, examples with matrices, pragmatic choices, and optimization algorithms.
Explores the importance of differentiating vector fields and the correct methodology to achieve it, emphasizing the significance of going beyond the first order.
Explores the dynamics of steady Euler flows on Riemannian manifolds, covering ideal fluids, Euler equations, Eulerisable flows, and obstructions to exhibiting plugs.
Introduces Manopt, a toolbox for optimization on smooth manifolds with a Riemannian structure, covering cost functions, different types of manifolds, and optimization principles.
Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.